Carlsen is less than 20 points away from immortality.

I didn't think Carlsen quite broke his rating record with Zurich; I guess I was wrong!

I understand the argument that of course these 20 points will be considerably harder than before, but for me, that just isn't enough to give me any serious doubt that he will cross 2900; in fact I think it'll only take a few years or less.

I mean, I thought the same thing when Carlsen was 2850 -- it's harder for him to keep going farther the higher his rating goes up -- yet he has still managed to do it. In general I think he really is that good at chess. I don't blame people for being sceptical -- I think no one should believe in something just on appearances, but the justification for thinking he will get to 2900 has a much stronger basis than mere appearances.

2900 may or may not be easy for him, but even at this time I don't think Carlsen has reached some sort of limit yet -- he loves the game, has continued to improve over the last two years, and it just doesn't seem implausible to think that this young man can continue to bloom to a noticeable degree -- unlike Fischer he's not the type to just become world champion and sit on it -- he clearly wants to remain a chess player. And certainly his 2860-2880 ratings have not been a fluke -- he has maintained these sorts of ratings for some time now. He just needs one more push -- maybe not as easy as it looks, but definitely doable for Magnus. And even if he doesn't maintain 2900 (though I think in the future he will), good form could easily bring him there temporarily.

And I'm saying all of this as someone who thinks rating inflation at the top levels is basically an illusion. For someone who believes in rating inflation the answer to the OP is even simpler!

You misunderstand the rating system, my friend. It's quite simple: If he plays only above 2700, his results will be worse, but the punishments for bad results are lower. If he plays people below 2700, yes his punishments are higher, but the chances of the bad result goes down.

Let's put it this way: If you play someone 100 points lower than you in a 100 game blitz match, if the ratings actually reflect your relative abilities, your ratings should stay the same by the time it's over. If you played someone 100 points higher instead, the ratings would still stay the same -- the fact that you will score worse is compensated by the fact that you don't need to score as high to maintain your rating.

He has immortality now being a world champion.  Heck we still know Smyslov and Euwe.  His playing strength is probably higher than his rating but he doesn't have enough competition to obtain his actual rating. 

Apparently, "my friend", you don't understand the ratings dynamics of a Fischer or Carlsen-like gap over the competition ;)...

Carlsen already enjoys a hefty advantage over the 2700+ GMs, so he can play in very strong and small events and still score very well, and gain ratings slowly while risking almost nothing...which is by far the best way to climb up while already holding #1.  

If he played in 2500+ large events, one loss to a 2600s GM would set him back months...and he would be playing a lot more games and it would happen.

You don't have to believe me...just believe Carlsen's behavior.  He understands this ratings phenom from the #1 position a lot better than you.

What will be Carlsens next tournament?

btickler is just another carlsen hater....who thinks he isn't that good, its getting quite pathetic

why would he play in 2500 + tournaments what does he have to gain from that

immortality? you underestimate infinity.

"Carlsen routinely avoids events with anyone rated below 2700 to avoid the hits his rating would take. He has gotten some criticism for it, in fact. That's why his rating is as high as it is now"

I rather think he avoids weak events because he finds it more rewarding to play stronger opponents. It isn't that long ago many said that Carlsen's rating would be lower if he only played top players, and now that he does that his rating would supposedly be lower if he played weaker opponents. I think his rating would be approximately the same regardless who he played, but in any case I don't find it strange that he doesn't see much of a challenge in playing events with lots of 2500s and 2600s. Aronian, Kramnik and Anand doesn't play such events either.

Varelse1, his next tournament will be the Gashimov Memorial in April, http://www.chess.com/news/vugar-gashimov-memorial-in-april-6274 Magnus Carlsen, Fabiano Caruana, Hikaru Nakamura, Sergey Karjakin, Shakhriyar Mamedyarov and Teimour Radjabov are in the field, so it's very strong (average around 2780). 

Then he plays the Norway Chess Tournament in June. This is shaping up to be one of the strongest tournaments of all time, with 7 of the current Top 10 playing, including Aronian, Kramnik, Caruana, and Svidler. It's possible the entire field will just be the Top 10, as 3 players are yet to be announced.

Following this, he'll probably play the 4-man Sinquefield Cup, which is also super strong, and then he'll play the World Championship match in November. 

So, for the entire year, the weakest player he'll face is likely to be Radjabov (ELO 2713), though he was close to 2800 this time last year. Apart from him, he's unlikely to face anyone under 2740, which is fair enough considering he's at 2881. Most GMs at 2760 wouldn't play many 2620 GMs either.

Tyvm, Pdub

Yeah, but the foregoing discussion about ratings assumes a constant skill curve, f'=c, but that's not necessarily the case. Lots of reasons, in fact, to think this breaks down. For example, 50 wins and 50 draws may be equal to 75 wins and 25 losses, but qualitatively, there's a big difference between the types of players who get these kinds of results. 

If you're much stronger than your opponent and you play a very double-edged style, then you're unlikely to get a result like +75-25 (if you're good enough to win 75 games, then it's not likely that you'll lose 25 along the way). But a safety-first type of player who's vastly stronger than his opponent may very plausibly get +50=50. 

For example, notice that great match players (e.g., Kramnik, Karpov, Petrosian) are not always the best tournament players, and vice versa. Also, there are other asymmetries -- for example, Morozevich just eats 2600 players for lunch, but his results against other 2700+ are less impressive. 

The weird reality is that chess skill is affected by a lot of factors, and the probabilistic character of the strengths of individual players is highly heterogeneous. Example: Kramnik was really tough for Kasparov to play; Kramnik struggled against Shirov; and Kasparov totally dominated Shirov. If skill were a single valued object, then that sort of "violation" of the principle of transitivity shouldn't occur, but it happens all the time. This suggests that while a particular ELO number may be a good prediction of my results against opponents in some range, it may be a poor predictor of my results against opponents in a different range. So if you wanted to be really accurate (I'm not suggesting that anyone do this in practice), you'd need multiple ELO ratings to express your strength against a variety of opponents of differing strengths. (e.g., you could say that I perform at 1750 when facing opponents rated 1600 or below, that I perform like 1850 when facing opponent rated 1601-1900, and that I perform like 1700 against opponents rated 1901 and above).

It is plausible that for some players, strategically entering some events rather than others may artificially bump up or diminish their ratings. But at that level, I doubt they care that much about their precise rating number. They're probably more interested in winning X or Y tournament rather than hitting some arbitrary rating number, so I doubt there's much gaming of the ratings system, and my intuition is that most ratings are reasonably accurate reflections of overall strength.

And for the record, despite what I've written above, I think Carlsen's results look very balanced. I don't think he performs noticeably better (than ratings would predict) when the competition is very strong or very weak. He seems to win more against weaker competition at the rate that his rating would predict. So, I do think it is not an issue in this particular case, although I disagree that we can just assume it away. The math alone cannot establish the fact, because it makes several simplifying assumptions that aren't obviously the case.

All you have done was repeat your original point, which I had already addressed. If you actually comprehended my post, you would know exactly how I would address what you are saying now (my response being that a higher penalty for losing is balanced out by the games being easier). You arbitrarily weight the higher penalty for losing as more important than the games being easier, but mathematically there need not be any difference (style could affect this, but it's unlikely -- generally, skill is skill, and it'll show no matter who you play).

Maybe Magnus would lose to one of those 2600 GMs... or maybe he would win a bunch of easy games in a row and get a huge rating increase -- either case is perfectly plausible.

I refer you back to the 100 game blitz match hypothetical I gave you.

Great post Daniel_Pi.

Daniel Pi: Of course there is variation. Some people you do better against than others, perhaps even contrary to what ratings suggest. But on average the ratings work great. If I do really poorly against one guy who has a similar rating to me but do perfectly well against others at my rating, yeah, I'm going to think that one guy I do badly against is an anomaly.

By your "it's all relative" logic, Carlsen could play any rating range with exactly the same risk level.  Or any player could play any other range and expect the exact win/loss ratio that the ratings spread dictates.  

This is a simplistic understanding of the ratings system.  What you are talking about is true on a macro level only, not on an individual level.  There are ways to exploit the system, and Carlsen knows this.

"There are ways to exploit the system, and Carlsen knows this"

Wijk last year must have been a lapse of judgment though, since he faced five below 2700 players there. His score against them was 5/5, by the way.

Yeah, but it could be systematic variation. Like you could just do badly on average against all players in a certain rating interval, relative to how you perform against average players of a different interval. That's not just an anomoly at that point, it's systematic deviation. It just suggests that a mathematical model of chess strength should have multiple values.

But that might get ridiculously complicated. I am inclined to agree with you that ELO as it is tends to get it right vastly more often than not, and possibly more accurate complications are not worth the additional computation cost. 

@Post#62: I'm not unaware of anomalies based on, say, style. I just don't think they are as important to consider as others think.

For example, I'm well aware that a 1900 player might have a bad score against a 1700 player simply based on style differences, but I think these cases are very uncommon, perhaps noticed more due to cognitive bias. On one hand we have different styles as players; but at the same time, we have to do a lot of the same stuff to improve. The dull truth is that mostly, what makes a person higher rated, is they simply make less mistakes. They see more tactics. They know more endgames. Chess players have more in common with each other than they think. No matter what kind of positions you like, this process of learning more tactics, learning more endgames, making less mistakes, is absolutely ubiquitous and an incredibly huge component of your rating.

Basically, I just don't think in practice this systematic variation you are talking about is likely to happen. As I have said, more or less, chess is chess. Why do I beat lower rated players? Because I see something they didn't. Every time. "Seeing something my opponent didn't" may be a very general way to put it, but it's pretty much how things work. You simply have more knowledge than your opponent, and it's bound to show. Again, weird combinations of style may make for strange cases, but they are indeed strange.

I'm speaking from experience here, as someone who has experienced anomalies, but, as one might expect, only rarely. I am a pretty safe player; this means I get less losses but more draws. I could do just as well getting more losses but less draws, as others at my rating might do.

Fabelhaft wrote: "It isn't that long ago many said that Carlsen's rating would be lower if he only played top players, and now that he does that his rating would supposedly be lower if he played weaker opponents."